# Adv-BNN: Improved Adversarial Defense through Robust Bayesian Neural Network

## TL;DR

This paper introduces Adv-BNN, a Bayesian neural network approach that learns a robust model distribution to defend against adversarial attacks, achieving state-of-the-art results on CIFAR-10 and ImageNet.

## Contribution

The paper proposes a novel adversarial training method using Bayesian neural networks to optimally incorporate randomness and improve robustness against attacks.

## Key findings

- Achieves 14% accuracy improvement on CIFAR-10 under PGD attack.
- Outperforms previous adversarial training methods on ImageNet.
- Demonstrates the effectiveness of Bayesian modeling in adversarial defense.

## Abstract

We present a new algorithm to train a robust neural network against adversarial attacks. Our algorithm is motivated by the following two ideas. First, although recent work has demonstrated that fusing randomness can improve the robustness of neural networks (Liu 2017), we noticed that adding noise blindly to all the layers is not the optimal way to incorporate randomness. Instead, we model randomness under the framework of Bayesian Neural Network (BNN) to formally learn the posterior distribution of models in a scalable way. Second, we formulate the mini-max problem in BNN to learn the best model distribution under adversarial attacks, leading to an adversarial-trained Bayesian neural net. Experiment results demonstrate that the proposed algorithm achieves state-of-the-art performance under strong attacks. On CIFAR-10 with VGG network, our model leads to 14\% accuracy improvement compared with adversarial training (Madry 2017) and random self-ensemble (Liu 2017) under PGD attack with $0.035$ distortion, and the gap becomes even larger on a subset of ImageNet.